Alberto Vilar, the arts patron and investment adviser, was in financial straits late last year. He owed money to contractors and his dry cleaner, according to friends, and was behind on paying the maintenance fee on his 11,000-square-foot, duplex apartment in Manhattan.

Yet in December, the co-founder of Amerindo Investment Advisors Inc., a formerly highflying money-management firm, confidently assured Columbia University Medical Center that his firm was on the upswing, according to physicians who attended a meeting with him....